Noise injection tests performed on HD 128621 to evaluate the performance of our shell framework in mitigating stellar activity depending on the continuum signal-to-noise ratio, S∕N_cont. The cross-validation algorithm to select only shell basis components with significant variance was disabled and five componentswere used for the fitted model. Top left: correlation between the noise-affected shell basis coefficients α_j and their respective coefficients without extra-noise injected α_j,obs. A shell basis component can be considered as recovered once its related coefficient α_j exceeds a correlation value with α_j,obs higher than (dotted line). This threshold was selected as the level that the shell basis component α₅, which is associated with noise in the observations, never reaches. Top middle: RV rms of the projected α_j (t) on the raw RV time series. Top right: RV rms of the residual RVs linearly decorrelated from the shell basis coefficients α_j (blue), as well as RV rms of the fitted RV activity model (red). The result for four different interesting S∕N_cont values (vertical lines): 50, 150, 250 and 350 are discussed in detail in the text. Bottom: periodograms of the residual RVs obtained after our shell framework correction for the four selected S∕N_cont levels. The periodogram of the uncorrected RVs are displayed in black as a comparison. The power of each periodogram was normalised by the 1% FAP level.